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Multiphysics Analysis of Trapped Field in Multi-Layer YBCO Plates

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Multiphysics Analysis of Trapped Field in Multi-Layer YBCO Plates Excerpt from the Proceedings of the COMSOL Conference 2009 Boston MultiPhysics Analysis of Trapped Field in Multi-Layer YBCO Plates Philippe J. Masson1 1Advanced Magnet Lab *1720 Main Street, Bldg. #4, Palm Bay, Fl-32905, [email protected] Abstract: superconductors have the unique configuration specifically developed for this capability of trapping magnetic flux. This feature specific application. The paper presents a FEA has the potential to enable and improve several electromagnetic-thermal analysis of flux trapping applications including high power density in YBCO multi-layers plates using COMSOL rotating machines. Current material used as MultiPhysics. trapped flux magnets (TFM) is single domain YBCO that present numerous limitations in 2. Flux trapping in superconductors terms of performance, stability and size. One way to overcome the limitations is to use thin Because of their unique properties, layers of YBCO deposited on disks and stack superconductors can trap magnetic flux and act them. Multi-layer trapped flux magnets were as “permanent” magnets. The phenomenon can successfully modeled and analyzed using be explained by the critical state model in which COMSOL MultiPhysics through coupled current density can only be ±Jc or 0. Since electromagnetic and thermal transient magnetization of superconductors is hysteretic in simulations. Simulations allow for a better nature, the magnetic state of the material understanding of how the current redistributes depends of the temperature and external field during thermal disturbances and validate the history. potential of the technology. Keywords: trapped flux magnets, 2.2 Flux trapping methods superconductors, YBCO, non-linear problem Several methods to trap magnetic flux in a 1. Introduction superconductor can be used. Their effectiveness and practicality differ from one method to Trapped Flux Magnets (TFM) are very another. attractive for application to power devices. The • Field cooling major limitation of flux trapping capabilities of bulk YBCO stems from mechanical problems. Field cooling consists of a cool down of the Indeed, Lorenz forces can become very superconductor under applied field. This method important when stored magnetic energy is very effective but requires a large magnet increases. As most of the stress is applied locally generating at least the value of flux density on pinning centers in the material, a failure desired in the superconductor. usually results in destruction of the material structure. In order to improve flux trapping • Zero field cooling capability in TFMs, mechanical reinforcement can be done using epoxy impregnated fiber glass If zero-field cooling is performed, the cloth and a record of 17 T trapped at 29 K was superconducting material will first react by achieved. However, due to the ceramic nature of shielding flux variation and will expel magnetic YBCO, it remains structurally weak and can very flux from its volume. The method then requires likely fail if electro-thermal instabilities occur. full saturation in current and necessitates large We have studied the feasibility of TFMs based magnets providing at twice the value of flux on multi-layer configurations that could be density desired in the superconductor. achieved by stacking disks made of coated conductors. The multi-layer configuration would • Pulsed magnetization bring a much better stress distribution and should lead to more stable flux trapping. Even though Pulse magnetization is identical in principle to packing factor remains an issue for stacked zero field cooling, however, because the flux coated conductors, it is expected that YBCO can variation is very fast, the superconductor can be deposited advantageously in multiple layer enter a flux flow regime and generate losses decreasing the magnitude of the critical current the super conductor without adding weight or density. Additionally, the method r equire s volume to the machine. An example of such energy storage for pul se generation . machine is shown in figure 1 [2]. The machine takes advantage of the flux trapping capability of • Flux pumping superconducting plates to create, shape and concentrate magnetic flux leading to a very high Recently flux pumping techniques have been power density. developed requiring a c omplex to set up , controllable temperature and magnetic gate material . This method represents a very promising alternative as no large field source is needed. Field cooling is the most eff ective way to trap magnetic flux in a superconducting material. After a field cooling, a superconducting plate behaves like a permanent source of magnetic field. Its major differences with permanent magnets are: Figure 1. Illustration of Bean’s model • a much larger magnetization • operation at constant flux instead of 4. Properties of YBCO constant magnetization (trapped flux magnets cannot be “defluxed”) The most widely used material in TFMs is YBCO. YBCO is a ceramic that become s Table 1: Field cooling of a superconducting plate Step 1 Step 2 Step 3 superconducting below 92 K and exhibits very high current density in single domain blo cks. A Bext = B max Bext = B max Bext = 0 T > T c T < T c T < T c flux density of 17 T has been trapped in a small YBCO plate at 29 K [3]. While bulk YBCO is a very attractive option, it presents severe limitations: • Brittle material that can develop cracks • Stress applied by the Lorentz forces on pinning centers ca n lead to mechanical 3. Applications of TFMs failure • Size limited to a few centimeters with Trapped flux magnets enable the development of homogeneous properties several superconducting devices requiring • Cannot be bent constant magnetic flux or large values of magnetic flux density. • Magnetic bearings Some applications, such as flywheels or high speed electrical machines, require frictionless bearings. TFMs can be advantageously used as they can provide very large forces and do not require active control. Indeed, since the magnetic flux intrinsically re mains constant, any variation Figure 2. Single grain YBCO c ylinder (www.can.cz) is automatically compensated by induced persistent currents. Superconductors exhibit a highly non -linear • Rotating machines electrical conductivity as shown in figure 3 and High specific power rotating machine require equation (3). large excitation field that can be produced by TFMs [1] . The major challenge is to magnetize n(B,T ) • J Improved flux pinning • Larger systems can be built E = Ec (3) J c ()B,T 5.00E-04 4.50E-04 4.00E-04 3.50E-04 3.00E-04 2.50E-04 E (V/m) 2.00E-04 1.50E-04 1.00E-04 5.00E-05 Figure 3. YBCO conductor from American 0.00E+00 50 70 90 110 130 150 Superconductor Inc. [4] I (A) Commercially available wide conductors can be used, Figure 3. E(I) characteristic of superconductors however, the stabilization layers necessary for stable conductor operation are not requires in TFM and a The critical current density of YBCO is higher filling factor can be achieved with a dedicated depending on the temperature and on the applied configuration. magnetic flux density. It can be parameterized as follows: 6. Problem definition B − T 1 90 1− 6.1 Geometry TB J c (B,T ) = J c )0,0( 1− e (4) Tc The system is modeled in 2D with axial The parameters J c(0 T, 0 K), T c and T b can be symmetry, which is a valid approximation for the obtained experimentally. Current flows in the a-b system of interest since YBCO can be deposited plane of the material and current density in the c- uniformly. The geometry implemented in axis of the material is negligible. COMSOL is shown in figure 4. Axis Field coil 5. Multilayer configuration TFM YBCO YBCO can be deposited in thin films and turned Epoxy resin into tapes. YBCO is the basis for second generation conductors or coated conductors and can be deposited on large areas. Up to 10 centimeter wide ribbons are currently manufactured and cut into 4 mm wide tapes to make conductors. Disks coated with YBCO film can be manufactured and stacked to form Heater cylinders. The electrical properties would then be Figure 4. Geometry implemented in Comsol strongly anisotropic as current is allowed to flow only in parallel planes (a-b planes) and no The system is modeled with homogeneous YBCO current is flowing between layers. YBCO is layers 0.15 mm thick and separated by 0.1 mm layers deposited on substrate and the filling factor of a of resin insulation. stack is a lot less than 50 %. However, current density in YBCO films or thin layers is orders of 6.2 Material properties magnitude larger than in large block and therefore compensate for the low filling factor. • YBCO Such a configuration brings numerous advantages: YBCO exhibits non-linear electrical and thermal • Material can be bent properties. In COMSOL, conductors are • Intrinsically mechanically reinforced modeled with their electrical conductivity, based on equation (3), the conductivity of YBCO can 6.3 Mesh, Sources and boundary conditions be expressed as follows. The mesh, represented in figure 7, is composed 3 1 2 −1 2 n of about 80,000 elements leading to a system J c0 T 1 E σ[S / m] = 1− with over 300,000 degrees of freedom. The mesh E T B E c c 1+ c is kept coarse in the surrounding air and in the B 0 (5) field coil. Where T c is the critical temperature, J c0 is the value of the critical current density at 0 K and 0 T, E c is the electrical field magnitude defining Jc, B 0 and n are determined experimentally. The electrical field E is a parameter of the electrical conductivity which would pose a problem in most FEA package but COMSOL allows for this dependence to be modeled. Specific heat and thermal conductivity of YBCO Figure 7. Mesh in the multi-layer component are plotted as a function of temperature in figure 5.
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